Spectral Analysis of a Chaotic Map Based on the Hyperbolic Tangent Function

Carlos Souza,Daniel Chaves,Cecilio Pimentel,João Evangelista

doi:10.14209/jcis.2016.9

Abstract

This work generalizes the chaotic map recently introduced by the authors with the addition of two new control parameters. The Lyapunov exponent is employed to analyze the chaotic dynamics of the proposed map. The spectral characteristics of chaotic signals generated by this map as a function of the control parameters are also investigated. The proposed map can be used in symbolic dynamics based communication systems with advantages over current approaches based on piecewise linear maps.

Highlights

Chaotic signals are known for its irregularity, aperiodicity, decorrelation and broadband [2]
They can be generated by simple deterministic dynamical systems [3], which motivate their application in cryptography [4], random number generation [5], watermarking [6], communications [7] and systems modeling [8]
The latter scheme is employed in a chaotic communication system [13], allowing to trade performance and security by using a piecewise linear chaotic map with a parameter that controls the length of a never visited region

Summary

INTRODUCTION

Chaotic signals are known for its irregularity, aperiodicity, decorrelation and broadband [2]. The information symbols are encoded into a chaotic sequence generated by a forward iteration of a chaotic map [10], [11], while the second method employs a backward iteration [12] as a way to avoid problems with error amplification and precision truncation found in the former scheme The latter scheme is employed in a chaotic communication system [13], allowing to trade performance and security by using a piecewise linear chaotic map with a parameter that controls the length of a never visited region (known as a guard region). The guard region restricts the chaotic system dynamics due to the length of this region, which invariably induces a compromise between performance and security This limitation is eliminated by the map proposed by the authors in [17].

SYMBOLIC DYNAMICS MODULATION

THE STANH MAP

THE CHAOTIC BEHAVIOR

SPECTRAL BEHAVIOR

CIRCUIT IMPLEMENTATION

CONCLUSIONS